\documentclass[]{article}
\setlength{\pdfpagewidth}{8.5in} \setlength{\pdfpageheight}{11in}
\begin{document}

 \setcounter{table}{1} 
\begin{table}[htbp] 
  \caption{\bf  Weak Factors:  local  PCA vs constant-PCA  ($T=24,r_{t-1}=2$)}
\medskip
\setlength{\tabcolsep}{3pt}
\centering
\begin{tabular}{|| c c c c c c   ||} 
\hline $ \#  \, factor $ & $cor( {\scriptstyle \tilde{\bf F}_s ,\tilde{\bf H}_{T-1}' {\bf F}_s  })  $ & $cor({\scriptstyle  \tilde{\bf F}_s^0 ,\tilde{\bf H}^{0 \prime} {\bf F}_s } )  $ &  $( {{\scriptstyle \tilde{\bf H }_{T-1}'  \bar{\bf F} \over \tilde{\bar{\bf F }}}}-1 )\%  $ &  $( {{\scriptstyle \tilde{\bf H }^{0 \prime}  \bar{\bf F} \over \tilde{\bar{\bf F }}^0}}-1 )\%  $  
    &  $\left( {{\scriptstyle  \tilde{\bf H}_{T-1}^{-1}  \tilde{\bf \Sigma }_\Lambda \tilde{\bf H}_{T-1}^{-1 \prime} \over (\tilde{\bf H}^{0})^{-1}  \tilde{\bf \Sigma }^0_\Lambda (\tilde{\bf H}^{0})^{-1 \prime}   }  } \right)  $      \\ [0.5ex] 
 \hline\hline
 $ \# 1  $ & 0.99 & 0.02 &  0.03& -86.65  &    3.54  \\ 
$ \# 2 $ & 0.99 &  0.11 &  -0.51 &    -212.79           &  26.82  \\ 
 \hline
\end{tabular}
        \parbox{7in}{\footnotesize{Each row reports  in columns two, three, four, five, and six, respectively,  the correlation between the local-PCA  \newline  risk factor ($\tilde{\bf F}_s$) and the   true (rotated) risk factor, and between         the constant-PCA risk factor  ($\tilde{\bf F}_s^0$) and the  \newline  true (rotated) risk factor 
        (averaged across $T$ and $T+T^0$ periods, respectively),  the bias (in per cent)  of the \newline local-PCA risk premia and the constant-PCA risk premia, and the ratio between local-PCA and  \newline constant-PCA cross-averaged squared (rotated) risk exposures (Monte Carlo averages, $M=1,000$ replications).  \newline  Row one (two) row corresponds to the first (second) risk factor, respectively.}}
\label{Table3}
\end{table}


\end{document}
